In this work, we derive coefficient bounds for the symmetric Toeplitz matrices T2(2), T2(3), T3(1), and T3(2), which are known first four determinants a new family of analytic functions with Borel distribution series in open unit disk U. Further, some special cases results obtained also pointed.

A starlike function f is characterized by the quantity $$zf'(z)/f(z)$$ lying in right half-plane. This paper deals with sharp bounds for certain Toeplitz determinants whose entries are coefficients of functions which takes values specific subset The results obtained include several new special cases and some known results.

Abstract. We investigate the simplest class of hyperdeterminants defined by Cayley in the case of Hankel hypermatrices (tensors of the form Ai1i2...ik = f(i1+i2+· · ·+ik)). It is found that many classical properties of Hankel determinants can be generalized, and a connection with Selberg type integrals is established. In particular, Selberg’s original formula amounts to the evaluation of all Ha...

The objective of this paper is to gain some insight into how well sparsity is preserved under determinant computations. For a square matrix A whose elements are indeterminates x1, . . . , xn and zeros, the determinant det(A) is a polynomial in x1, . . . , xn with integer coefficients. We derive an upper bound on the number of monomials in det(A) for a class of determinants which includes bigrad...

Abstract We obtain an asymptotic formula for $$n\times n$$ n × Toeplitz determinants as $$n\rightarrow \infty $$ → ∞ , non-negative symbols with any fixed number of Fisher–Hartwig singularities, which is uniform respect to the location ...

‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.